1. Field of the Invention
The present invention relates to signal processing apparatus, such as image processing apparatus, for providing variable-bandwidth filtering of a D-dimensional signal (where D may have a given value equal to or larger than one) and, more particularly, to such apparatus capable of providing a linearly variable response over a wide range of cutoff frequencies with linear phase.
2. Description of the Prior Art
It is known to apply various types of signal processing to signals to extract certain features of interest for further analysis. Usually, linear filtering is the main tool used in such applications, such as low-pass, band-pass, or high-pass filtering a signal to remove high, mid, or low frequencies respectively. Further, in many cases it is advantageous to interactively vary the cutoff of the filter to isolate features of interest, so that a variable bandwidth filter is desirable.
Typically, in one-dimensional (1D) signal enhancement, such as in enhancing horizontal frequencies in a television picture, analog or digital filters can be used. Variable-bandwidth analog filters are known in the art. However, providing a linearly variable response over a wide range of cutoff frequencies with the added desirable property of linear phase is extremely difficult and costly in the case of variable-bandwidth analog filters. Variable-bandwidth digital filters (which can be implemented by switching in a different set of filter coefficients for each new cutoff frequency) are to be preferred because they can have precisely linear phase over their entire range of operation, and they can be made completely stable under all conditions. However, one problem with such implemented variable-bandwidth digital filters is that the number of coefficients needed to represent a wide range of various cutoff frequencies can grow extremely large depending on the degree of incremental "fineness" of the variation from one cutoff frequency to another.
The use of filtering in two-dimensional (2D) image enhancement applications is known. Another problem that occurs in such 2D image enhancement applications is the need to store multiple points vertically for filtering. In raster-scanned images, where adjacent vertical points are one full scan line apart, this means storing a number of successive lines in order to access the points needed for a filtering. In analog filter implementations, at most one to two lines are possible. This is usually achieved using CCD (charge-coupled delay) delay lines, which are costly. In digital filter implementations, the storage is achieved with digital memories, which are less expensive and more robust than CCD delay lines.
It is known in signal theory that a filters' bandwidth is inversely related to its time response. That is, as the passband is made more narrow the corresponding time response of the filter gets longer. In the case of vertical filtering, low frequencies can only be extracted by using many lines of storage. This can be very expensive. The cost and complexity of doing this with analog filters would be prohibitive.
A known technique (disclosed in U.S. Pat. No. 4,674,125) for solving such vertical-filtering imaging problems is to use Laplacian pyramidal processing. In Laplacian pyramidal processing, a signal is decomposed in multiple, octave-wide, spatial-frequency bands; wherein the frequency decomposition inherently produces bands of information containing one octave of frequency, where adjacent bands touch on octave boundaries. This approach relies on repetitive usage of low-pass filter-subsample operations, so that the means for high-order low-frequency filtering is accomplished very efficiently and cost-effectively.
A problem with octave decomposition that occurs in known Laplacian pyramidal processing results from integer subsampling by two at each level of the pyramid. This imposes a severe limitation on the processing of some signals. For optimal spectral decomposition, it is desirable to produce band-pass (or low-pass) components that are not octave wide to better match the information of interest. For example, in image transmission a technique called progressive transmission is sometimes used. The signal is first put into a Laplacian pyramid format, and the lower-resolution images are transmitted quickly due to their relatively low quantity of data. As bandwidth permits, refinements of the image (the higher frequency band-pass components) are sent and added in at the receiver to reconstruct the original image. This process assures that the receiver always displays a full image, although initially a blurred version of the original is displayed which becomes clearer if and when later-received higher frequency band-pass components are added to the display.
Using the Laplacian pyramid to process a 2-D image means that the amount of data in each band increases from band-to-band by a factor of four (two per dimension.) In moving up to the higher resolution bands, the increase in data by four may be too much for the channel to handle, while for instance, an increase in two might not. Thus, there is a great advantage in scaling the quantity of data as needed, and not be limited to the fixed octave-width sizes of the spatial-frequency bands forced by the aforesaid known Laplacian pyramid technique.
Further, reference is made to our copending U.S. patent application Ser. No. 08/033,503, filed Mar. 18, 1993, entitled "Resampling Apparatus Suitable for Resizing a Video Image", which is assigned to the same assignee as the present application, the disclosure of which is incorporated herein by reference.